Application of Interpolating Matrix Method to Study Dynamics of Axially Moving Beams Made of Functionally Graded Materials

In this paper, the divergent instability and coupled flutter characteristics of axially moving beams made functionally graded materials (FGM) are studied using interpolation matrix method. The material property beam is designed to change smoothly continuously along thickness direction. considering Euler-Bernoulli theory, Hamilton’s principle used derive differential equation transverse vibration kinematics FGM beams. addition, calculation model for solving complex frequency based on method has been established. presented solutions compared with those in literature illustrate effectiveness results show that divergence velocities tend decrease increase gradient index, there a very narrow stability region between first static (divergence) dynamic (first- second-order flutter).